Questions tagged [grammars]

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9
votes
1answer
750 views

Do there exists polynomial size CFG that describe this finite language?

Do there exists permutations $\pi_1,\pi_2$ and polynomial size (in $|w|=n$) context free grammar that describe the finite language $\{w \pi_1(w) \pi_2(w)\}$ over alphabet $\{0,1\}$? UPDATE: For one ...
15
votes
1answer
421 views

Lower bounds on the size of CFGs for specific finite languages

Consider the following natural question: Given a finite language $L$, what is the smallest context-free grammar generating $L$? We can make the question more interesting by specifying a sequence of ...
19
votes
6answers
1k views

Which models of computation can be expressed through grammars?

This is a reformulation of Are grammars programs? previous asked by Vag and with many suggestions from the commenters. In what way can a grammar be seen as specifying a model of computation? If, for ...
30
votes
2answers
2k views

Is {$a^{i}b^{j}c^{k} ~|~ i \neq j, i \neq k, j \neq k$} non-context-free?

Is the language {$a^{i}b^{j}c^{k} ~|~ i \neq j, i \neq k, j \neq k$} context-free or not? I realized that I have encountered almost all variants of this question with different conditions about the ...
14
votes
4answers
596 views

Base-k representations of the co-domain of a polynomial - is it context-free?

In chapter 4 of Jeffrey Shallit's A Second Course in Automata Theory the following problem is listed as open: Let $p(n)$ be a polynomial with rational coefficients such that $p(n) \in \mathbb{N}$ for ...
13
votes
0answers
1k views

Is CFL strictly contained in NL?

We know that $\mathsf{REG}=\mathsf{NSPACE}(O(1))$ and $\mathsf{CSL}=\mathsf{NSPACE}(O(n))$. What is the relation of $\mathsf{CFL}$ and $\mathsf{NSPACE}(O(\log n))=\mathsf{NL}$? Is $\mathsf{CFL}$ a ...
5
votes
1answer
2k views

Emptiness of PDA without constructing the corresponding CFG

The emptiness problem for Context free Grammars(CFG) is well studied. The same holds for the equivalence problem between Pushdown Automata (PDA) and CFGs. Therefore, given a PDA, the straightforward ...
8
votes
2answers
345 views

Mistake in Wikipedia CSG example?

I'm confused about the example given in Wikipedia article about Context-sensitive grammar: https://en.wikipedia.org/wiki/Context-sensitive_grammar Disclamer: I've already changed discussed section ...
1
vote
0answers
315 views

Restricted read twice BDDs and context free grammars

Several papers give poly-time algorithms for constrained paths on labelled graphs, e.g. [1] Quote: Given an alphabet Σ, a (directed) graph G whose edges are weighted and Σ-labeled, and a formal ...